Developer xDPx has released a GUI tool named PSP HD GUI, which allows you to repack PSP isos into an fpkg. The aim is to run PSP games on your (hacked) PS4 within its integrated PSP emulator (PSPHD).
It’s important to note that this is just a GUI that helps making the process of installing PSP isos on the PS4 easier, not that it will magically make them work better: running PSP games on the PS4 appears to be somewhat possible, but compatibility so far has proven to be very low. PS3Dev Wiki has a PSP on PS4 compatibility page which reports that 5 out of 37 tested games so far actually run in a playable state.
Nevertheless, such a GUI could help people give it a try themselves, and confirm whether or not a larger portion of the PSP library could ultimately run on hacked PS4s.
Download PSP HD GUI
PSP HD Gui 1.0 can be downloaded from the developer’s github here. Please note that at the time of writing, we have not tested this tool.